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****MATHEMATICS RELATIONS QUIZ-5**

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

**MATHEMATICS RELATIONS QUIZ-5**

**Q1.**If f:R→R and g:R→R are defined by f(x)=2x+3 and g(x)=x

^{2}+7, then the values of x such that g(f(x) )=8 are

Solution

We have, g(f(x) )=8 ⇒g(2x+3)=8 ⇒(2x+3)

We have, g(f(x) )=8 ⇒g(2x+3)=8 ⇒(2x+3)

^{2}+7=8⇒2x+3=±1⇒x=-1,-2**Q2.**Let A be a set containing 10 distinct elements, then the total number of distinct function from A to A is

Solution

Given a set containing 10 distinct elements and f:A→A

Given a set containing 10 distinct elements and f:A→A

Now, every element of a set A can make image in 10 ways.

∴ Total number of ways in which each element make images =10

^{10}.**Q3.**If the functions f and g are defined by f(x)=3x-4,g(x)=3x+2 for x∈R, respectively then

g

^{-1}(f^{-1}(5) )=
Solution

Solution

**Q6.**36. The relation R={(1,1),(2,2),(3,3)} on the set {1, 2, 3} is

Solution

The relation R={(1,1),(2,2),(3,3)} on the set {1,2,3} is an equivalent relation.

The relation R={(1,1),(2,2),(3,3)} on the set {1,2,3} is an equivalent relation.

**Q8.**If f:R→R is defined by f(x)=x-[x]-1/2 for x∈R, where [x] is the greatest integer not exceeding x, then {x∈R:f(x)=1/2} is equal to

Solution

**Q9.**Consider the following relations R={(x,y)│x, y are real numbers and x=wy for some rational number w};S={(m/n,p/q)|m,n,p and q are integers such that n,q≠0 and qm=pn}. Then

Solution

Solution

For f(x) to be defined, x-4≥0 and 6-x≥0 ⇒ x≥4 and x≤6 Therefore, the domain is [4, 6].

For f(x) to be defined, x-4≥0 and 6-x≥0 ⇒ x≥4 and x≤6 Therefore, the domain is [4, 6].